Simplify (x^4)^(1/2).

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Multiple Choice

Simplify (x^4)^(1/2).

Explanation:
Raising a power to another power multiplies the exponents: (x^4)^(1/2) = x^(4 × 1/2) = x^2. Another way to see it is to view it as the square root of x^4, that is sqrt((x^2)^2). The square root yields the nonnegative value, so sqrt((x^2)^2) = |x^2|. Since x^2 is always nonnegative, |x^2| = x^2. So the simplified form is x^2.

Raising a power to another power multiplies the exponents: (x^4)^(1/2) = x^(4 × 1/2) = x^2. Another way to see it is to view it as the square root of x^4, that is sqrt((x^2)^2). The square root yields the nonnegative value, so sqrt((x^2)^2) = |x^2|. Since x^2 is always nonnegative, |x^2| = x^2. So the simplified form is x^2.

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